Solve for HL hypotenuse leg theorem
-GEOMETRY

Answer:

21

Step-by-step explanation:

1/5 x 21 = 21/5

Answer:

[tex]\huge{\mathfrak{Solution}}[/tex]

[tex]\huge{\bold{ \frac{ {y}^{2} }{36} - \frac{ {x}^{2} }{121} = 1 }}[/tex]

[tex]\huge{\bold{ \frac{(y - k) {}^{2} }{ {a}^{2} } - \frac{(x - h) {}^{2} }{ {b}^{2} } = 1 \: is \: the \: standard \: equation \: with \: center \: (h ,k),semi-axis \: a \: and \: semi-conjugate \: -axis \: b.}}[/tex]

[tex]\huge\boxed{\mathfrak{We \: get,}}[/tex]

[tex](h,k) = (0,0),a = 6,b = 11[/tex]

[tex]For \: hyperbola \: assymtoms \: are \: y = + \frac{a}{b} (x - h) + k[/tex]

[tex]Therefore,y = \frac{6}{11} (x - 0) + 0,y = - \frac{6}{11} (x - 0) + 0[/tex]

[tex]\large\boxed{\bold{y = \frac{6x}{11},y = - \frac{6x}{11} . }}[/tex]

If y²/36 - x²/121 = 1, the asymptotes are y = (36/121) x and y = -(36/121) x.

To find the equations for the asymptotes of the hyperbola represented by the equation y²/36 - x²/121 = 1, we can compare it with the standard form of a hyperbola:

(y - k)² / a² - (x - h)² / b² = 1

where (h, k) represents the center of the hyperbola.

In the given equation, we have y²/36 - x²/121 = 1. To put it in standard form, we need to divide both sides by 1 (which is essentially dividing by 1 on the right side):

y²/36 - x²/121 = 1 / 1

Now, we can see that a² = 36 and b² = 121.

To find the equations of the asymptotes, we use the center (h, k) and the values of a and b. The asymptotes of a hyperbola have equations of the form:

y = k ± (a/b)(x - h)

In this case, the center (h, k) is (0, 0), a² = 36, and b² = 121:

The equations for the asymptotes are:

y = 0 ± (36/121) x

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A possible solution to the inequality is 2 hotdogs and 8 tacos.

Let x represents the number of hotdogs purchased and y represents the number of tacos purchased.

Gabriella has $30 to spend and must buy a minimum of 9 hotdogs and tacos altogether.

Hence:

4x + 2y ≤ 30    (1)

x + y ≥ 9      (2)

Also:

x ≥ 2   (3)

A possible solution to the inequality is 2 hotdogs and 8 tacos.

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Answer:

The expression is d(45) + 25 = c

Step-by-step explanation:

The expression is d(45) + 25 = c. Let's test it out to see if it is correct. We will test it out by substituting d and c.

Day 1:

Day 2:

Day 3:

Day 4:

Therefore, the expression is d(45) + 25 = c.

Hoped this helped.

Answer:

 1-2y+y^2

Step-by-step explanation:

(1–y)^2

(1-y) * (1-y)

FOIL

first: 1*1 =1

outer: 1*-y = -y

inner: -y *1 = -y

last: -y*-y = y^2

Add together: 1+-y-y+y^2  

Final answer1-2y+y^2

Credit:

wegnerkolmp2741o

He solved it earlier.

Answer:

the value of y+2 is 21+2=24y

Answer:

7inches.

Step-by-step explanation:

the properties of a square is that it has the same length and width (and height. but height isn't needed here).

since the area is 50.4 inch^2, square root this value,

[tex]\sqrt{50.4}[/tex]=7inches.

Answer:

Our material is 54" wide. Here is a helpful chart to help you quickly convert linear yards into inches and feet.

How big is one linear yard of fabric?

Yards Length Width

3 108 Inches (9 Feet) 54 Inches (4.5 Feet)

4 144 Inches (12 Feet) 54 Inches (4.5 Feet)

Step-by-step explanation:

C A R R Y

O N

L E A R N I N G

Answer:

22

Step-by-step explanation:

2x+x-2=2x+9

3x-2=2x+9

x-2=9

x=11

MN=2x

MN=2(11)

MN=22

The equation that represents the partial sum of the geometric series is 125, 25, 5, 1

Given the partial sum of a geometric sequence expressed as:

[tex]\sum\left { n=4 \atop {n=1}} \right. 125(\frac{1}{5} )^{n-1}[/tex]

If n = 1, the

a(1) = [tex]125(\frac{1}{5} )^{1-1}\\[/tex]

a(1) = [tex]125(\frac{1}{5} )^{0}\\[/tex]

a(1) = 125

If n = 2

a(2) = [tex]125(\frac{1}{5} )^{2-1}\\[/tex]

a(2) = [tex]125(\frac{1}{5} )^{1}\\[/tex]

a(2) = 25

If n = 3

a(3)= [tex]125(\frac{1}{5} )^{3-1}\\[/tex]

a(3) = [tex]125(\frac{1}{5} )^{2}\\[/tex]

a(3) = 5

If n = 4

a(4)= [tex]125(\frac{1}{5} )^{4-1}\\[/tex]

a(4) = [tex]125(\frac{1}{5} )^{3}\\[/tex]

a(4) = 1

Hence the equation that represents the partial sum of the geometric series is 125, 25, 5, 1

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Answer:

a

Step-by-step explanation:

Answer:

Write the equation of the line in slope-intercept with a slope of 1 and passing through the (0,-1)

y = x - 1

Write the equation of the line in slope-intercept with a slope of 4 passing through the (-2,1)

y = 4x + 9

Step-by-step explanation:

Write the equation of the line in slope-intercept with a slope of 1 and passing through the (0,-1)

y = mx + b

if slope is 1, m= 1

y = x + b

if passing through (0,-1), then y = -1, x = 0

-1 = (0) + b

b = -1

then

y = x - 1

Write the equation of the line in slope-intercept with a slope of 4 passing through the (-2,1)

y = mx + b

if slope is 4, m= 4

y = 4x + b

if passing through (0,-1), then y = 1, x = -2

1 = 4(-2) + b

b = 9

then

y = 4x + 9

Answer:

75-82=-7

Step-by-step explanation:

e

Answer:

1:2 by division of 5

10:9 by division of 6

Answer:

25X48=1200 buttons in all

1200 divided by 15 = 80

She needs to buy 80 bags which totals 1200 buttons

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

when p is 4

p² + 5 = 4² + 5

16 + 5 = 21

Answer:

c would be the closest due to the total amount of vitamin c in the objects.

The quantity of fruit which contains an amount of vitamin C closest to the combined content is: C. 1,800 g grams of pineapple.

In this exercise, we would determine the amount of vitamin C that is present in a combination of 50 grams of acerola cherries and 150 grams of kiwifruit.

For acerola cherries:

100 grams of acerola cherries = 1678 mg.

50 grams of acerola cherries = X mg.

Cross-mutiplying, we have:

X = 83,900/100 = 839 mg.

For kiwifruit:

100 grams of kiwifruit = 105 mg.

150 grams of kiwifruit = Y mg.

Cross-mutiplying, we have:

Y = 15,750/100 = 157.5 mg.

Combine vitamins = 157.5 + 839 = 996.5 mg.

Based on intuition, we would choose 1,800 grams of pineapple.

100 grams of pineapple = 56 mg

1,800 grams of pineapple = Z mg.

Cross-mutiplying, we have:

Z = 100,800/100 = 1008 mg.

Thus, 996.5 mg of vitamin C is closest to 1008 mg.

Note: If you do the above computations for other quantities of fruit, you'll get a value far from 996.5 mg.

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The shape of the graph of quadratic functions is the shape of a parabola.

The steps for drawing a graph of the function f(x) = 2·(x + 4)² - 3 arranged in the correct order are;

Reasons:

The given function is; f(x) = 2·(x + 4)² - 3

The function is given in the vertex form; f(x) = a·(x - h)² + k

Therefore, the vertex, (h, k) = (-4, -3)

Step (a);

The vertex can be plotted on the graph

Step (b);

Given that the quadratic term is 2·x², the pattern that can be used for the points from the vertex is therefore, 2·x²

From the vertex (-4, -3) apply the 2·x² pattern by going to the right 1 unit and  up 2 × 1² = 2 units to get the point (-4 + 1, -3 + 2) = (-3. -1)

Step (c);

To get the next point, the 2·x² pattern is applied with x = 2, to the vertex to get; (-4 + 2, -3 + (2×2²)) = (-2, 5)

Step (d);

A third point on the graph relative to the vertex is obtained again by applying the 2·x² pattern again to the vertex with x = 3, to get;

(-4 + 3, -3 + (2 × 3²)) = (-1, 15)

Step (e);

The axis of symmetry can be drawn with a vertical line passing through the vertex, which is the line, x = -4

The line x = -4 can be drawn on the graph next

Step (f);

The points obtained relative to the vertex (-3, -1), (-2, 5), (-1, 15) can reflected about the axis of symmetry x = -4, to get;

(-3, -1) [tex]\underrightarrow {R_{(x = -4)}}[/tex] (-5, -1)

(-2, 5) [tex]\underrightarrow {R_{(x = -4)}}[/tex] (-7, 5)

(-1, 15) [tex]\underrightarrow {R_{(x = -4)}}[/tex] (-7, 15)

Step (g);

The parabola that is U shaped can be drawn from the points plotted in the steps above.

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Answer:

  AB, CD

Step-by-step explanation:

Skew lines do not lie in the same plane, and do not intersect. One such pair is AB and CD.

__

Additional comment

Any of the lines, and any of the lines that intersect its diagonally-opposite edge will be skew lines.

For example, the opposite edge to line BC is line EG. Lines that intersect EG are ED, EF, GA, GH. All of those four lines are skew with respect to line BC.

Answer:

5

Step-by-step explanation:

5 =5 +5+5=5+5

Answer:

y=(5/3)x + 5

Step-by-step explanation:

Every line is in the form: y = ax+b. If some points are on this line, they satisfy this equation. So we can write:

-5 = a(-6) + b

0 = a(-3) + b

It's a system of equations. We can solve them by subtracting the second equation from the first:

-5-0 = -6a - (-3a) + b - b

That becomes:

-5 = -3a

Therefore:

a = 5/3

Now we plug this value in the second equation of the system, and find the value of b:

0 = 5/3*(-3) +b

b=5

The final line equation will be: y=(5/3)x + 5

y = [tex]\frac{5}{3}[/tex]x + 5

First, find the slope. The formula to find slope can be defined as [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].

Given points (-6, -5) and (-3, 0), we can substitute those values in and find that the slope for this line will be [tex]\frac{5}{3}[/tex].

Using slope-intercept form, our equation so far is y = [tex]\frac{5}{3}[/tex]x + b. To find b, we substitute the coordinates of any point and solve. Doing so gets us a value of 5 for b.

Therefore, our final answer is y = [tex]\frac{5}{3}[/tex]x + 5.

Answer:

MN=9.1 cm

LM= 9.9 cm

Step-by-step explanation:

Answer:

90lbs

Step-by-step explanation:

If Tim weights 90lbs, his brother must weigh 130lbs which add to make 220lbs

Answer:

b = [tex]\frac{7}{12}[/tex]

Step-by-step explanation:

b + [tex]\frac{2}{3}[/tex] = 1 [tex]\frac{1}{4}[/tex] ← change to an improper fraction

b + [tex]\frac{2}{3}[/tex] = [tex]\frac{5}{4}[/tex]

Multiply through by 12 ( the LCM of 3 and 4 ) to clear the fractions

12b + 8 = 15 ( subtract 8 from both sides )

12b = 7 ( divide both sides by 12 )

b = [tex]\frac{7}{12}[/tex]

Answer:

The value of b is 7/12.

Step-by-step explanation:

Question :

Solve for b.

[tex]{\implies{\sf{b + \dfrac{2}{3} = 1 \dfrac{1}{4}}}}[/tex]

Enter your answer as a fraction in simplest form in the box.

[tex]\implies{\sf{b = \square}}[/tex]

[tex]\begin{gathered}\end{gathered}[/tex]

Solution :

[tex]{\implies{\sf{b + \dfrac{2}{3} = 1 \dfrac{1}{4}}}}[/tex]

Converting the mixed fractions into improper fraction.

[tex]{\implies{\sf{b + \dfrac{2}{3} = \dfrac{(1 \times 4) + 1}{4}}}}[/tex]

[tex]{\implies{\sf{b + \dfrac{2}{3} = \dfrac{(4)+ 1}{4}}}}[/tex]

[tex]{\implies{\sf{b + \dfrac{2}{3} = \dfrac{4+ 1}{4}}}}[/tex]

[tex]{\implies{\sf{b + \dfrac{2}{3} = \dfrac{5}{4}}}}[/tex]

Now, transporting LHS to RHS.

[tex]{\implies{\sf{b= \dfrac{5}{4} - \dfrac{2}{3}}}}[/tex]

Taking LCM of denominators and subtracting.

[tex]{\implies{\sf{b= \dfrac{(5 \times 3) - (2 \times 4)}{12}}}}[/tex]

[tex]{\implies{\sf{b= \dfrac{(15) - (8)}{12}}}}[/tex]

[tex]{\implies{\sf{b= \dfrac{15 - 8}{12}}}}[/tex]

[tex]{\implies{\sf{b= \dfrac{7}{12}}}}[/tex]

[tex]{\star{\red{\underline{\boxed{\sf{b= \dfrac{7}{12}}}}}}}[/tex]

Hence, the value of b is 7/12.

[tex]\begin{gathered}\end{gathered}[/tex]

Verification :

[tex]{\implies{\sf{b + \dfrac{2}{3} = 1 \dfrac{1}{4}}}}[/tex]

Substituting the value of (b=7/12)

[tex]{\implies{\sf{ \dfrac{7}{12} + \dfrac{2}{3} = 1 \dfrac{1}{4}}}}[/tex]

Converting mixed fractions into improper fraction

[tex]{\implies{\sf{ \dfrac{7}{12} + \dfrac{2}{3} = \dfrac{(1 \times 4) + 1}{4}}}}[/tex]

[tex]{\implies{\sf{ \dfrac{7}{12} + \dfrac{2}{3} = \dfrac{(4) + 1}{4}}}}[/tex]

[tex]{\implies{\sf{ \dfrac{7}{12} + \dfrac{2}{3} = \dfrac{4 + 1}{4}}}}[/tex]

[tex]{\implies{\sf{ \dfrac{7}{12} + \dfrac{2}{3} = \dfrac{5}{4}}}}[/tex]

Taking LCM of denominators in LHS and adding.

[tex]{\implies{\sf{ \dfrac{(7 \times 1) + (2 \times 4)}{12} = \dfrac{5}{4}}}}[/tex]

[tex]{\implies{\sf{ \dfrac{(7) + (8)}{12} = \dfrac{5}{4}}}}[/tex]

[tex]{\implies{\sf{ \dfrac{7 + 8}{12} = \dfrac{5}{4}}}}[/tex]

[tex]{\implies{\sf{ \dfrac{15}{12} = \dfrac{5}{4}}}}[/tex]

Cutting the fraction to simplest form.

[tex]{\implies{\sf{ \cancel{\dfrac{15}{12}} = \dfrac{5}{4}}}}[/tex]

[tex]{\implies{\sf{ \dfrac{5}{4}= \dfrac{5}{4}}}}[/tex]

[tex]{\star{\red{\underline{\boxed{\sf{LHS = RHS}}}}}}[/tex]

Hence Verified!

[tex]\underline{\rule{220pt}{3.5pt}}[/tex]

[tex]A+B+C\\\\=(2x-y+3xy)+(x+2xy) +(3y+xy)\\\\=3x+2y+6xy[/tex]

The value of the expression A + B + C is equal to 3x - 2y + 4xy.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Are three expressions A = 2x - y + 3xy, B = x + 2xy and C = 3y + xy.

Now, A + B + C is equal to the sum of their values which is,

= (2x - y + 3xy) + (x + 2xy) + (3y + xy).

Now, we'll combine the like terms,

= 2x + x - y + 3y + 3xy + xy.

= 3x - 2y + 4xy.

So, The value of the expression A + B + C is equal to 3x - 2y + 4xy.

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Answer:

12x - 6

Step-by-step explanation:

4 + 15x - 10 -3x

(15x - 3x) + (4-10)

12x - 6

Answer:

48 degrees

Step-by-step explanation:

6y=8y-16

y=8

8(8)-16= ?

64-16=

Answer:

∠ P = 48°

Step-by-step explanation:

Since NM = PM then the triangle is isosceles with base angles being congruent, then

∠ P = ∠ N , that is

8y - 16 = 6y ( subtract 6y from both sides )

2y - 16 = 0 ( add 16 to both sides )

2y = 16 ( divide both sides by 2 )

y = 8

Then

∠ P = 8y - 16 = 8(8) - 16 = 64 - 16 = 48°